A method of this type is known from the book by H. Titze “Fehler und Fehlerschutz in elektrischen Drehstromanlagen”, [Faults and Fault Protection in Electrical Three-phase Systems], Volume 2, 1953, pages 223 to 227, particularly page 227. In this method, a breaker having one short-circuit detection device is provided at each end of a line section of an electrical energy supply line to be monitored. If the short-circuit detection devices detect a fault in the line section to be monitored, they actuate the associated circuit breakers by means of a tripping signal whereupon the breakers open by separating the line section from the energy supply line. A re-closing device, particularly a re-closing relay, ensures that the breaker at the one end of the line section is closed again after a short time by delivery of a re-closing command. During this process, actuation of the re-closing device also trips the breaker at the other end of the line section and thus also closes it. In the method, therefore, the two breakers at the ends of the line section to be monitored are re-closed quasi-synchronously.